Task-based imaging systems

ABSTRACT

A method for generating an output image of a scene is disclosed. A detector of a task-based imaging system includes a plurality of pixels, and the scene includes at least one object located at a given object distance within a range of object distances between the object and the imaging system. The method includes capturing a high resolution image of the scene, converting the high resolution image into an image spectrum of the scene, determining a defocused optical transfer function (OTF) of the imaging system over the range of object distances and determining a pixel modulation transfer function (MTF) over the plurality of pixels. The method also includes multiplying the image spectrum with the OTF and the MTF to generate a modified image spectrum of the scene, converting the modified image spectrum into a modified image of the scene, and generating the output image from the modified image.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of, and claims the benefitof priority to, commonly-owned and U.S. patent application Ser. No.11/524,142, filed 19 Sep. 2006 now U.S. Pat. No. 7,944,467 and entitled“Task-Based Imaging Systems,” which claims priority to U.S. ProvisionalPatent Application No. 60/718,522, filed 19 Sep. 2005 and entitled “IrisRecognition at a Large Standoff Distance,” and U.S. Provisional PatentApplication No. 60/779,712, filed 6 Mar. 2006 and entitled “Zoom LensSystems with Wavefront Coding.” U.S. patent application Ser. No.11/524,142 is also a continuation-in-part of commonly-owned U.S. patentapplication Ser. No. 11/225,753 entitled “Iris Image Capture Devices andAssociated Systems,” filed 13 Sep. 2005 and now U.S. Pat. No. 7,652,685,which claims priority to U.S. Provisional Patent Application No.60/609,445, filed 13 Sep. 2004 and entitled “Iris Recognition Securityfor Camera Phones, Digital Cameras and Personal Digital Assistants.”U.S. patent application Ser. No. 11/524,142 is also acontinuation-in-part of U.S. patent application Ser. No. 11/000,819entitled “System and Method for Optimizing Optical and Digital SystemDesigns,” filed 1 Dec. 2004 and now U.S. Pat. No. 7,469,202, whichclaims priority to U.S. Provisional Patent Application No. 60/526,216,filed on 1 Dec. 2003 and entitled “Designing Optical Imaging Systemswith Wavefront Coding Elements.” Each of the aforementioned patentapplications is expressly incorporated herein by reference in itsentirety.

U.S. GOVERNMENT RIGHTS

A portion of the embodiments disclosed herein was made with Governmentsupport under a subcontract of grant number DAAD 19-00-1-0540, grantedby the Army Research Office to Wake Forest University. The Governmenthas certain rights herein.

U.S. patent application Ser. No. 10/810,446, filed 25 Mar. 2004 andentitled “Mechanically-Adjustable Optical Phase Filters for ModifyingDepth of Field, Aberration-Tolerance, Anti-Aliasing in Optical Systems”and PCT Patent Application Serial No. PCT/US06/09958 filed 20 Mar. 2006and entitled “Imaging Systems with Pixelated Spatial Light Modulators”are expressly incorporated herein by reference in their entireties.

The following U.S. patents are expressly incorporated by reference intheir entireties: U.S. Pat. No. 5,748,371, entitled “Extended Depth ofField Optical Systems” to Cathey et al.; U.S. Pat. No. 6,525,302,entitled “Wavefront Coding Phase Contrast Imaging Systems” to Dowski,Jr., et al.; U.S. Pat. No. 6,873,733, entitled “Combined WavefrontCoding and Amplitude Contrast Imaging Systems” to Dowski, Jr.; U.S. Pat.No. 6,842,297, entitled “Wavefront Coding Optics” to Dowski, Jr.; U.S.Pat. No. 6,911,638, entitled “Wavefront Coding Zoom Lens ImagingSystems” to Dowski, Jr., et al.; and U.S. Pat. No. 6,940,649, entitled“Wavefront Coded Imaging Systems” to Dowski, Jr.

BACKGROUND

One goal of a task-based imaging system may be to provide task-specificinformation or image data for one or more signal-processing tasks. Suchtasks may include biometric iris recognition, biometric facerecognition, biometric recognition for access control, biometricrecognition for threat identification, barcode reading, imaging forquality control in an assembly line, optical character recognition,biological imaging, automotive imaging for object detection and fiducialmark recognition for registration of objects during automated assembly.The above-mentioned biometric recognition tasks, for instance, may beexecuted by task-based imaging systems for security or access purposes.As an example, biometric iris recognition can provide humanidentification with very high accuracy when optical and digital portionsof such a task-based imaging system provide image data that is detailedenough and has a high enough signal-to-noise ratio (“SNR”).

The performance of a task-based imaging system is known to be directlyrelated to an SNR of image data that is required for successfulcompletion of the task. The SNR is in turn related to thecharacteristics of the imaging system. Characteristics that affectsystem performance include spherical and other aberrations, defocus,variations in magnification, depth of field, chromatic aberration,alignment tolerances, dynamic vibrations and temperature variations.These characteristics can cause the system to have a task-specific SNRthat is smaller than that of a diffraction-limited system.

Certain systems described in the prior art perform iris recognition atshort distances, using small apertures; see, for example, R. Plemmons etal., “Computational imaging systems for iris recognition,” in Proc.SPIE, August 2004. However, while such systems are effective for shortstandoff distances, they may use small lens apertures, which lead to lowsignal levels (i.e., low SNR) and relatively low resolution; suchsystems may not be suitable for longer standoff distances.

SUMMARY

In one embodiment, a task-based imaging system for obtaining dataregarding a scene for use in a task includes an image data capturingarrangement for (a) imaging a wavefront of electromagnetic energy fromthe scene to an intermediate image over a range of spatial frequencies,(b) modifying phase of the wavefront, (c) detecting the intermediateimage, and (d) generating image data over the range of spatialfrequencies. The task-based imaging system also includes an image dataprocessing arrangement for processing the image data and performing thetask. The image data capturing and image data processing arrangementscooperate so that signal-to-noise ratio (SNR) of the task-based imagingsystem is greater than SNR of the task-based imaging system withoutphase modification of the wavefront over the range of spatialfrequencies.

In another embodiment, a task-based imaging system for obtaining dataregarding a scene for use in a task includes at least one opticalelement for (a) imaging a wavefront of electromagnetic energy from thescene to an intermediate image and (b) modifying phase of the wavefront,and a detector for detecting the intermediate image and for generatingimage data over a range of spatial frequencies. The optical element isconfigured for cooperating with the first detector so that the SNR ofthe task-based imaging system is greater than SNR of the task-basedimaging system without phase modification of the wavefront over therange of spatial frequencies. In an embodiment, the task is selected asat least one of biometric iris recognition, biometric face recognition,biometric recognition for access control, biometric recognition forthreat identification, barcode reading, imaging for quality control inan assembly line, optical character recognition, biological imaging andautomotive imaging for object detection.

In a further embodiment, a method for generating an output image of ascene captured by a detector of a task-based imaging system isdisclosed. The detector includes a plurality of pixels and the sceneincluding at least one object located at a given object distance withina range of object distances, which object distance is defined as adistance between the object and the task-based imaging system. Themethod includes capturing a high resolution image of the scene over arange of spatial frequencies, converting the high resolution image intoan image spectrum of the scene, determining a defocused optical transferfunction (OTF) of the task-based imaging system over the range of objectdistances, and determining a pixel modulation transfer function (MTF)over the plurality of pixels of the detector. The method furtherincludes multiplying the image spectrum with the OTF and the MTF togenerate a modified image spectrum of the scene, converting the modifiedimage spectrum into a modified image of the scene, and generating theoutput image from the modified image.

In still another embodiment, a method for use with a task-based imagingsystem includes imaging electromagnetic energy from a scene to anintermediate image of the task-based imaging system, modifying phase ofa wavefront of the electromagnetic energy, detecting the intermediateimage, and generating image data over a range of spatial frequencies,based on the intermediate image so detected such that SNR of thetask-based imaging system is greater than SNR of the task-based imagingsystem without modifying phase over the range of spatial frequencies.

In yet another embodiment, a method for optimizing the task-basedimaging system for obtaining data regarding a scene for use in a taskover a range of object distances is disclosed. The scene includes atleast one object located within the range of object distances, whichobject distance is defined as a distance between the object and thetask-based imaging system. The method includes: 1) determining a targetSNR of the task-based imaging system; 2) specifying a set of pupilfunction parameters and a merit function; 3) generating a new set ofpupil function parameters based on the merit function so specified; 4)determining SNR over a range of object distances; 5) comparing the SNRto a target SNR; and 6) repeating steps 2) through 5) until the SNR isat least equal in value to the target SNR.

In a further embodiment, an improvement in a task-based imaging systemfor obtaining data regarding a scene for use in a task is disclosed. Thetask-based imaging system includes at least one optical element, forimaging a wavefront of electromagnetic energy from the scene to anintermediate image, and a detector for detecting the intermediate imageand for generating image data over a range of spatial frequencies. Theimprovement includes a phase modification element for modifying phase ofthe wavefront such that the SNR of the task-based imaging system isgreater than a SNR of the task-based imaging system without the phasemodification element.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may be understood by reference to the followingdetailed description taken in conjunction with the drawings brieflydescribed below.

FIG. 1 illustrates a security scene wherein task-based imaging systemsmay be used in accordance with the present disclosure.

FIG. 2 illustrates a security scene showing co-operational,multifunction task-based imaging systems in accordance with the presentdisclosure.

FIG. 3 illustrates a security scene showing non-permanent installationof co-operational, multifunction task-based imaging systems inaccordance with the present disclosure.

FIG. 4 illustrates a security scene showing handheld multifunctiontask-based imaging systems in accordance with the present disclosure.

FIG. 5 is an illustration of part of a human eye including features ofinterest for biometric recognition.

FIG. 6 is an illustration of part of a human face including features ofinterest for biometric recognition.

FIG. 7 is a series of images of 2-D barcodes comparing images capturedwith imaging systems with and without wavefront coding.

FIG. 8 is a series of gray-scale images of text comparing imagescaptured with imaging systems with and without wavefront coding.

FIG. 9 is a series of binary images of text comparing images capturedwith imaging systems with and without wavefront coding.

FIG. 10 is a gray-scale image of objects on an assembly line capturedwith an imaging system without wavefront coding.

FIG. 11 is a gray-scale image of objects on an assembly line capturedwith an imaging system with wavefront coding.

FIG. 12 shows a scene wherein task-based imaging systems used to detectobject via automotive imaging may be used in accordance with the presentdisclosure.

FIG. 13 is an image of a Drosophila embryo that was stained formicrotubules during mitosis, illustrating how spatial frequencies ofinterest within biological systems may be enhanced or maintained forimaging and recognition purposes.

FIG. 14 is a pair of diagrammatic illustrations of an imaging system infirst and second states for providing variable optical power by the useof a slidable optical element configuration and variable wavefrontcoding by the use of dual rotating phase filters.

FIG. 15 is a block diagram showing a task-based imaging system inaccordance with the present disclosure.

FIG. 16 is a contour plot of the surface sag of an exemplary wavefrontcoding element suitable for use in iris recognition at a large standoffdistance in accordance with the present disclosure.

FIG. 17 is a graphical plot of the number of pixels that subtend animage of an iris as a function of standoff distance to the imagingsystem for iris recognition.

FIG. 18 is a graphical plot of the number of waves of defocus over thestandoff distance range for an imaging system.

FIG. 19 is a series of graphical plots of simulated, through-focusnormalized point spread functions (PSFs) for an imaging system includingwavefront coding in accordance with the present disclosure.

FIG. 20 is a series of graphical plots of simulated, through-focus MTFsfor an imaging system including wavefront coding in accordance with thepresent disclosure.

FIG. 21 is a contour plot of the polar-MTF of an exemplary imagingsystem including wavefront coding in accordance with the presentdisclosure.

FIG. 22 is a graphical plot of the mean contrast at the spatialfrequencies of interest for an imaging system, as a function of standoffdistance, averaged over all directions (−π to +π), for an imaging systemincluding wavefront coding in accordance with the present disclosure.

FIG. 23 is a graphical plot of the mean SNR at the spatial frequenciesof interest for an imaging system, as a function of standoff distance,averaged over all directions (−π to +π), for an imaging system includingwavefront coding in accordance with the present disclosure.

FIG. 24 is a graphical representation of a filter used to process imagescaptured by an imaging system, for an imaging system including wavefrontcoding in accordance with the present disclosure.

FIG. 25 is a flow diagram showing a process for the generation ofsimulated images comparable to those captured by an imaging system thatincludes wavefront coding, in accord with an embodiment.

FIG. 26 is a block diagram showing a system for the optimization of atask-based imaging system including wavefront coding.

FIG. 27 is a flow diagram showing a process for the optimization of atask-based imaging system including wavefront coding, in accord with anembodiment.

FIG. 28 is a series of schematic diagrams showing the relative positionsof an original image, a PSF and a down-sampled image as seen by a givenimaging system.

FIG. 29 is pair of plots detailing effects of aliasing with regard tothe varied origin of the down-sampling.

FIG. 30 shows a series of simulated iris images that incorporate theeffects of a wavefront coding element and related processing inaccordance with the present disclosure.

FIG. 31 shows a graphical plot of Hamming distances as a function ofstandoff distances (2 m to 2.5 m) for simulated images captured by animaging system without wavefront coding.

FIG. 32 shows a graphical plot of Hamming distances as a function ofstandoff distances (2 m to 2.5 m) for simulated iris images thatincorporate the effects of a wavefront coding element and relatedprocessing in accordance with the present disclosure, shown here toillustrate that the inclusion of wavefront coding provides a broaderrecognition range in comparison to the system without wavefront coding.

FIG. 33 is a schematic diagram of an experimental setup used foracquiring iris images.

FIG. 34 is series of graphical plots of experimentally obtained,normalized PSFs, for an imaging system including wavefront coding, inaccordance with the present disclosure.

FIG. 35 is a series of graphical plots of experimentally obtained,normalized MTFs corresponding to the normalized PSFs shown in FIG. 34.

FIG. 36 is a contour plot of the experimentally obtained, polar-MTF ofan exemplary imaging system including wavefront coding.

FIG. 37 is a graphical plot of an experimentally-obtained mean contrastat the spatial frequencies of interest for an imaging system includingwavefront coding, as a function of standoff distance, averaged over alldirections (−π to +π).

FIG. 38 is a graphical plot of Hamming distances as a function ofstandoff distance to an iris for iris recognition using an imagingsystem without wavefront coding.

FIG. 39 is a graphical plot of Hamming distances as a function ofstandoff distance to an iris for iris recognition using an imagingsystem including wavefront coding, in accord with an embodiment.

DETAILED DESCRIPTION OF DRAWINGS

Wavefront coding (“WFC”) enables high quality imaging over a range ofoptical aberrations including defocus; for example, WFC may enable animaging system to provide an image that is in focus over a wide range ofstandoff distances. One combination of WFC and biometric irisrecognition at short distances between a handheld device and an iris isdisclosed in U.S. Provisional Patent Application No. 60/609,445 and U.S.patent application Ser. No. 11/225,753.

Wavefront coding and related methods, such as certain computationalimaging methods, may reduce certain effects of system characteristicssuch as spherical and higher order aberrations, defocus, magnification,depth of field, chromatic aberration, alignment tolerances, dynamicvibrations and temperature variations. In WFC, the pupil function of theimaging system is modified in a way that maintains a system's ability tocapture image data over a large range of variation of thesecharacteristics. Additionally, WFC may be able to supply a visuallyacceptable (e.g., to a human viewer) image while providing the imagedata to be used in a specific signal-processing task

It is noted that, for purposes of illustrative clarity, certain elementsin the drawings may not be drawn to scale.

FIG. 1 shows a security scene 100 wherein task-based imaging systems maybe used. Within the scope of this disclosure, imaging system may beunderstood as any combination of cameras, system(s) of cameras, one ormore cameras and controller(s), camera(s) with associated opticalelements (lenses, etc.) and/or processors (e.g., processors orcomputers, optionally configured with software) that are required forthe task-based imaging application. Within security scene 100, a subject160 is approaching a controlled access-point (e.g., a door) 110 from adirection 150 (indicated by an arrow). Subject 160 must pass throughthree different zones 140, 130 and 120 defined within walls 115 to reachaccess point 110. In each zone 120, 130 and 140, there may be placed oneor more imaging systems such as an image data capturing arrangement 125in zone 120, an image data capturing arrangement 135 in zone 130 and animage data capturing arrangement 145 in zone 140. Each image datacapturing arrangement may perform single or multiple functions;alternatively, all imaging systems may perform the same function. Eachone of image data capturing arrangements images a wavefront ofelectromagnetic energy from the scene to an intermediate image, modifiesphase of the wavefront, detects the intermediate image, and generatesimage data over a range of spatial frequencies of interest. An exemplaryfunction that all imaging systems may perform is to biometricallyidentify subject 160. Such biometric identification may include irisrecognition and/or face recognition. Also, optionally, subject 160 maycarry a badge or another item (not shown) that may be identified by textor barcode recognition. Although security scene 100 and image datacapturing arrangements 125, 135 and 145 are discussed hereinafter withregard to specific types of electromagnetic energy sensitive sensors(such as, but not limited to, infrared (IR), long-wave infrared (LWIR),red-green-blue visible (RGB), etc.), it may be understood by thoseskilled in the art that actual wavelengths of the electromagneticspectrum used by the image data capturing arrangement may vary. Forexample an image data capturing arrangement that is generally designatedan IR system may respond to visible light, near infrared (NIR), mid-waveinfrared (MWIR), or LWIR. Imaging systems may also be designed to usenarrow or wide wavelength bands as required by the task to be performed.When imaging electromagnetic energy including a wavelength range, eachone of image data capturing arrangements 125, 135 and 145 may includeimaging and wavefront coding optics suitable for imaging and modifyingphase in different portions of the wavelength range.

When subject 160 is far from an imaging system, subject 160 is said tobe in the far field of that imaging system, such as when subject 160 isin zone 140 and is being observed by image data capturing arrangement125. In the far field, subject 160 is far enough away from the pupil ofthe image data capturing arrangement that an image of subject 160 takenby image data capturing arrangement 125 is nearly free of wavefrontaberration errors; in such a case, wavefront coding may not be necessaryto extend the depth of field. However, wavefront coding may still beincorporated into the image data capturing arrangement in order tocorrect for aberrations potentially caused by operating the image datacapturing arrangement at high magnification. For example, a modulationelement for modifying the phase of the wavefront (i.e., wavefrontcoding) may be incorporated into the image data capturing arrangementsuch that one or more of image aberrations in the task-based imagingsystem are reduced in comparison to the task-based imaging systemwithout the modulation element. If not corrected, such aberrations maydegrade SNR of spatial frequencies of interest that are required tosuccessfully complete a task. In some situations, high magnification(i.e., zoom) may be required to select the area (e.g., eyes or face) forrecognition of subject 160 from a larger imaged area of security scene100.

At close ranges, depth of field within an image of subject 160 becomesvery sensitive to wavefront aberration errors and may benefit from useof WFC to achieve good depth of field and a SNR, at the spatialfrequencies of interest, required for recognition. An example of such asituation is when subject 160 passes within 2 to 4 meters of an imagedata capturing arrangement such as image data capturing arrangement 135in security scene 100. In this case, to biometrically identify subject160, image data capturing arrangement 135 may be required to track amoving target and to automatically adjust the magnification and depth offield, and to maintain a SNR of the spatial frequencies of interestrequired for recognition.

At intermediate distances between subject 160 and an image datacapturing arrangement (e.g., one of imaging systems 125, 135 and 145)there may be greater depth of field and lower required magnificationsthan for close distances. These intermediate distances may requireintermediate degrees of wavefront coding to maintain the required SNR ofthe spatial frequencies of interest for recognition. Imaging systems145, 135 and 125 may cooperate successively or in parallel to track,isolate the face or eyes of and then biometrically identify subject 160.Access point 110 may then respond automatically to a positive biometricrecognition by one or more imaging systems 145, 135 and 125, and permitaccess by subject 160. Alternatively, access point 110 may deny accessbased on a positive biometric recognition of subject 160 as a threat.

FIG. 2 shows a security scene 200 showing co-operational, multifunctiontask-based imaging systems. Multi-channel, multi-optic imaging systems210 and 220 may provide preview and oblique views of a subject 260 withsecurity scene 200. Imaging systems 210 and 220 may be, for example,color visible electromagnetic energy imaging devices such as RGB and CMYimagers. Preview information provided by imaging systems 210 and 220 maybe communicated by wired (or wireless) pathways 290 to a centralizeddatabase, communications and control system 270. Control system 270 mayinclude wireless communication facility 280 for connection to othersystems (not shown). In place of or in addition to imaging systems suchas 220, control system 270 may directly control access and may keeprecords of access, such as time-stamped records of subjects. Thesecontrol systems and/or imaging systems may also include a data storageunit for storing information such as records of access and humanviewable images while simultaneously providing recognition data or otheroutput.

Preview information may be used to prepare an interrogation system foraccess control event. Preview information may include, but is notlimited to, such data as a low resolution image wherein a subject 260has been physically located but has not been biometrically recognized.Preview information may be transferred from, for instance, imagingsystems 210 or 220 to a multi-optic imaging system assembly 245 thatincludes imaging systems 230, 240 and 250 for further interrogation suchas biometric recognition. Imaging system 230 may be, for instance, amulti-channel imaging system forming a part of imaging system assembly245 that may be self-regulated (e.g., communicates internally viapathways 290) to perform a dedicated task. As part of the task, imagingsystems 230, 240 and 250 may transfer image data via pathways 290 toand/or from each other. Imaging system 230 may, for instance, includeoptics for two separate electromagnetic energy wavelength bands such asvisible RGB and LWIR. Imaging system assembly 245 may also includesensors operating in the IR (corresponding to imaging system 240) andgray scale (corresponding to imaging system 250).

FIG. 3 shows a security scene 300 showing a non-permanent installationof co-operational, multifunction task-based imaging systems 310, 320 and330. An RGB imaging system 310, a CMY imaging system 320 and an IRimaging system 330 may cooperate to biometrically identify a subject360. In an exemplary embodiment, imaging systems 310 and 320 providepreview information while imaging system 330 performs iris recognition.A wired (or wireless) pathway 390 provides interconnectivity for imagingsystems 310, 320 and 330. A wireless communication facility 380 connectsthe imaging systems to other systems. Wireless, portable, multi-channel,multi-optic systems such as formed by imaging systems 310, 320 and 330,pathway 390 and communication facility 380 may be used, for example, inapplications such as temporary security.

FIG. 4 shows a schematic diagram of a security scene 400 includinghandheld multifunction task-based imaging systems 410 and 420. Imagingsystems 410 and 420 are positioned to view a subject 460. Imaging system410 may be, for instance, a handheld portable single channel unit forlow cost (e.g., a cost low enough to be considered disposable) and maybe applied in unstable security installations. Imaging system 410 mayalso permit wireless communications via wireless communicationconfiguration 480. Imaging system 420 may be a handheld portablemulti-channel device for identification and recording use with awireless communication configuration 480. Imaging systems 410 and 420may be designed to be lightweight, ruggedized and tolerant of extremetemperatures during use and storage conditions.

Discussed immediately hereinafter in association with FIGS. 5-15 aremultiple applications of task-based imaging in accordance with thepresent disclosure. An exemplary task-based imaging applicationregarding iris recognition is discussed in detail in association withFIGS. 5 and 16-39. The methods, procedures, and apparatus discussedherein below with respect to iris recognition may be adapted to thedesign, optimization and use of other task-based imaging systems such asthose discussed in association with FIGS. 5-15, namely, biometric facerecognition, biometric recognition for access control, biometricrecognition for threat identification, barcode reading, imaging forquality control in an assembly line, optical character recognition,biological imaging and automotive imaging for object detection.

As an example of tasked-based biometric imaging, attention is directedto FIG. 5, which is an illustration of a part of a human eye 500. Humaneye 500 includes a pupil region 510, an iris region 520, a ciliarymuscle region 530 and a choroid region 540. It is known that iris region520 is unique between humans and may be used to identify individualswith a high degree of accuracy. Iris region 520 contains structures thathave spatial frequencies of interest for biometric recognition that maybe selectively enhanced using wavefront coding.

As another example of task-based biometric imaging, FIG. 6 shows anillustration of a part of a human face 600. Human faces, even amongidentical twins, may have distinguishing features that may be used forbiometric recognition. Features such as a width 610 of a head, a spacing620 of the eyes, a width 630 of an eye, a width 640 of a nose and awidth 650 of a mouth may provide specific spatial frequencies that maybe selectively enhanced using details of the present disclosure. Arecent survey of the topic of face recognition is provided by W. Zhao,et al., “Face Recognition: A Literature Survey,” ACM Computing Surveys,Vol. 35, No. 4, December 2003, pp. 399-458 and “Face Recognition Basedon Polar Frequency Features,” Y. Zana et al., ACM Transactions onApplied Perception, Vol. 3, No. 1, January 2006.

In addition to biometric imaging, other task-based imaging problems maybenefit from imaging systems including wavefront coding for enhancingspecific spatial frequencies. An example of such a task-based imagingproblem is barcode reading. Both 1D and 2D barcodes have patternedstructures that have defined periodicities and therefore specificspatial frequencies. FIG. 7 shows a series of images of 2-D barcodescomparing images captured with imaging systems with and withoutwavefront coding. Images 710-714 were collected from a imaging systemwithout wavefront coding. Images 720-724 were collected from a systememploying wavefront coding. The images captured by imaging systemsincluding wavefront coding show significantly less blurring andtherefore retention of spatial frequencies of interest for recognitionover a larger range of distances from best focus.

Still referring to FIG. 7, when discussing non-human subjects it iscommon to employ terminology such as “distance from best focus” in placeof a term such as “standoff distance”. A difference in the terminologiesmay be understood such that “standoff distance” is an absolute distanceand “distance from best focus” is a relative distance. That is, anequivalent standoff distance for a non-human subject may be determinedby adding/subtracting the distance (beyond/inside of) best focus to thebest focus distance. Images 710 and 720 were collected at best focusdistances. Images 711 and 721 were collected at distances 1 cm beyondthe best focus distance. Images 712 and 722 were collected at distances2 cm beyond the best focus distance. Images 713 and 723 were collectedat distances 3 cm beyond the best focus distance. Images 714 and 724were collected at distances 4 cm beyond the best focus distance. Images720-724 show significantly less blurring and therefore retention ofspatial frequencies of interest for recognition over a larger range ofdistances from best focus in comparison to images 710-714 taken with theimaging system without wavefront coding.

FIGS. 8 and 9 show two versions of the same series of images. The set ofimages 800 in FIG. 8 are gray-scale images and set of images 900 of FIG.9 are binary images. Comparing these images shows the contrast betweenhuman vision and imaging for optical character recognition. Human visiondifferentiates color and gray-scale. For optical characterization(“OCR”), images are processed into binary black and white images. Likebarcodes, printed text has specific spatial frequencies that are relatedto the font, font size and typeface. Images 810-812 and 910-912 werecollected using an imaging system without wavefront coding. Images820-822 and 920-922 were collected using an imaging system employingwavefront coding. Each column of images displays related similar imagescaptured at different distances from best focus. The top row images 810,820, 910 and 920 were collected at distances that were 10 cm less thanthe best focus distance. The center row images 811, 821, 911 and 921were collected at the best focus distance. The bottom row images 812,822, 912 and 922 were collected at distances 20 cm greater than the bestfocus distance. It may be readily seen, especially in the set of binaryimages 900, that the images captured by the imaging system includingwavefront coding exhibit enhanced spatial frequencies related to thetext, in comparison to the images captured without wavefront coding.Maintaining the spatial frequencies of the text characters provides fora higher probability of optical character recognition.

FIGS. 10 and 11 also compare images obtained using imaging systemswithout wavefront coding (FIG. 10) and imaging systems employingwavefront coding (FIG. 11). FIGS. 10 and 11 include gray-scale images1000 and 1100 of objects on an assembly line. For machine vision systemsto recognize objects of similar size and shape, high spatial frequencyinformation is advantageously maintained or enhanced by the imagingsystem. In image 1000 of FIG. 10, captured using an imaging systemwithout wavefront coding, a central region 1020 is well focused whereasregions 1010 and 1030 are considerably out of focus, indicating thatspatial frequency information has been lost in these outer regions. Incontrast, in image 1100 of FIG. 11, captured using an imaging systemincluding wavefront coding, all regions of image 1100 are in focus andthe spatial frequency information has been enhanced relative to that ofthe imaging system without wavefront coding.

FIG. 12 shows another type of task-based imaging system that may benefitfrom enhancing or maintaining spatial frequencies of interest forrecognition by including wavelength coding in the imaging system. FIG.12 shows a scene 1200 of an application of task-based imaging systemsspecifically for object detection via imaging at an automobile. In thisexample, an imaging system 1240 is incorporated into an automobile 1230.This type of imaging system may use, for instance, NIR, IR or LWIRelectromagnetic energy wavelengths to provide nighttime imagingcapabilities. Scene 1200 includes a pedestrian 1210 walking within theboundaries of a crosswalk 1220. Imaging system 1240 may be designed torecognize crosswalk 1220 such that, upon recognition of crosswalk 1220,the imaging system may then determine if pedestrian 1210 is present inthe crosswalk. Increasing the ability of imaging system 1240 torecognize crosswalk 1220 decreases the chance that automobile 1230 mayhave contact with pedestrian 1210. A crosswalk is generally indicated bypainted stripes or an inset array of bricks or stones. Therefore, sincecrosswalk 1220 has specific spatial frequencies resulting from itsconstruction, wavefront coding may be included into imaging system 1240in order to maintain or enhance those frequencies to aid recognition byimaging system 1240.

Another category of task-based imaging applications that may benefitfrom enhancing spatial frequencies of interest is biological imaging. Asan example of biological imaging, FIG. 13 is a fluorescence image 1300of a Drosophila embryo whose synchronously dividing nuclei have beenstained to show microtubules during mitosis. The image has been invertedfor viewability. The microtubules are the multiple small dark featuresin the image. Microtubules are tiny subcomponents of cells and are longtubes 24 to 25 nanometers in diameter. They form part of the cellularstructure known as the cytoskeleton. During mitosis, microtubulesdynamically form into bundles to create the mitotic spindle on which thechromosomes move. An exemplary mitotic spindle structure is enclosed ina box 1310. The thread-like spindle microtubules can be resolved usingan optical microscope and identified by their characteristic structure.Microtubules provide physical structure and mediate the dynamicalprocess of cell division. Improper functioning of microtubules can leadto chromosomal separation or segregation defects. Properly recognizingmicrotubules and any irregularities therein may provide a researcherwith information about the details of mitosis. The addition of wavefrontcoding to an imaging system such as that used to monitor microtubulesduring mitosis may enhance or maintain spatial frequencies of interestand aid recognition of irregular microtubules.

As discussed in reference to FIGS. 1-4, an imaging system may berequired to adapt to multiple different tasks or situations. Forexample, an imaging system may initially be required to provide data forfacial recognition; such recognition may require only limited depth offield. Then, at a later time, the same system may be used for irisrecognition, requiring more depth of field. Alternatively, the imagingsystem may be required to capture conventional (human viewable) imageswithout utilizing wavefront coding. Two exemplary methods for achievingsuch adaptable imaging systems are by changing focus (zoom capability)and by altering the wavefront coding applied, as now described.

In particular, FIG. 14 shows a pair 1400 of diagrammatic illustrationsof an imaging system that provides variable optical power by utilizing aslidable optical element configuration and variable wavefront coding bythe use of dual rotating phase filters. In illustration 1402, theimaging system is in a first state and electromagnetic energy reflectedor emanating from an object 1410 is imaged through an aperture 1420 ontoa detector 1470 as an intermediate image 1465. In accordance with theintermediate image, detector 1470 generates image data 1475 (representedby an arrow) over a range of spatial frequencies present in the object.Slidable elements 1430 may cooperate with an element 1460 to modify themagnification of object 1410. Additional elements 1440 and 1450 may be,for instance, rotating phase filters for varying the wavefront coding ofthe image. Slidable elements 1430, additional elements 1440 and 1450and/or element 1460 modulate phase of a wavefront of electromagneticenergy from the object (i.e., wavefront coding). Image data fromdetector 1470 may be further processed by a digital signal processingunit (DSP) 1480, which then outputs desired data. Alternatively, imagedata 1475 from detector 1470 are directly output as data 1490. Data 1490may be output by either pathway or by both pathways. Data 1490 processedby DSP 1480 may produce a final human viewable image whereas data 1490that is not processed by DSP 1480 may be used for recognition or othertasks. The phase modification of the electromagnetic energy wavefrontmay be provided by one or more of slidable elements 1430, additionalelements 1440 and 1450 and element 1460 alters characteristics of theintermediate image such that the SNR of imaging system 1400 is greaterthan the SNR of the imaging system without the phase modification.Alternatively, or additionally, the phase modification may be configuredto cooperate with DSP 1480 so as to reduce at least one imagingaberration (e.g., temperature-dependent aberration and impact-inducedaberration) in the imaging system, in comparison to the same imagingsystem but without the phase modulation and the digital signalprocessor. In illustration 1404, the imaging system is in a second stateof magnification and wavefront coding. Slidable elements 1430 as well asrotating phase filter 1450 (shown by different hatching) are indifferent positions with respect to similar elements 1430′ and 1450′ ofillustration 1402, thereby generating a different intermediate image1465′, image data 1475′ and data 1490′.

Although discussed in association with rotating phase elements, thevariable wavefront coding elements may be designed from reflective ortransmissive optical elements such as liquid crystal spatial lightmodulators, deformable mirrors, liquid lenses, liquid crystal variators,slidable optical element configurations, sliding variator arrangements,sliding aperture variators or other electro-mechanical (i.e., digitallight processing (DLP)) or electro-optical means to alter the phase.Phase variation of the electromagnetic energy wavefront in the range ofzero to ten waves or more may be required depending upon the specificapplication. Alternatively, optical elements that modify the amplitudeof the wavefront may be employed in place of phase modifying elements.Furthermore, adaptive systems may be used in task-based imaging systemssuch as those designed for biological imaging. For example in FIG. 13,microtubules were being imaged utilizing a microscope; in suchapplications it may be necessary to observe larger or smaller cellstructure within the same imaging system (e.g., by changingmagnification). Furthermore, wavefront coding may be used to correct forimaging aberrations in the task-based imaging system; for example, amodulation element for modifying the phase of the wavefront (i.e.,wavefront coding) may be incorporated into the image data capturingarrangement as at least one of one or more of slidable elements 1430,additional elements 1440 and 1450 and element 1460 such that one or moreof image aberrations in the task-based imaging system are reduced incomparison to the task-based imaging system without the modulationelement.

FIG. 15 is a block diagram 1500 showing a task-based imaging system1510. Imaging system 1510 includes an image data capturing arrangement1520 and an imaging data processing system 1530. Exemplary imagingsystems are, for instance, imaging systems of 210 and 220 of FIG. 2 andimaging system assembly 245 working in cooperation with systemcontroller 270.

Image data capturing arrangement 1520 may include, but is not limitedto, apparatus, systems and processes for capturing image data from ascene. Components that may be included in system 1520 are, for example,illumination sources, optical elements such as reflective, refractiveand holographic elements, phase modifying elements such as thatdescribed in association with FIG. 16, variable optical elements such asthose described in association with FIG. 14, detectors (e.g., sensorsand cameras) and other accessory hardware that may be required tosupport the image data capturing arrangement.

Image data processing arrangement 1530 may include, but is not limitedto, apparatus, systems and processes for processing image data that wascaptured by image data capturing arrangement 1520 from a scene.Components that may be included in system 1530 are camera-basedprocessors, system controllers such as 270 of FIG. 2, externalcomputers, software codes, operating systems, image processing software,wavefront coding filter designs, task-based software programs and datastorage units for recording the image data.

Exemplary details of enhancing or maintaining spatial frequencies ofinterest in a task-based imaging system (such as described above) byemploying wavefront coding may be more clearly understood in the contextof iris recognition at a large standoff distance, as now described.Certain difficulties arise in the implementation of biometric irisrecognition when an iris to be imaged is at a large standoff distance(e.g., greater than two meters). When the iris to be imaged is locatedgreater than about a meter away from the imaging system, the imagingsystem should have a large aperture in order to: 1) provide high spatialfrequency information, so as to image the details of the iris; and 2)capture enough light to produce a high quality signal. Increasing theaperture of the imaging optics leads to a reduction in depth of field,making the use of wavefront coding even more beneficial when the subjectis at a large standoff distance. Also, high modulation over a spatialfrequency range of interest and a defocus range of interest is desiredfor large standoff distance applications; for such applications,wavefront coding can be utilized to increase modulation over that whichwould be available without wavefront coding.

Increased field of view and depth of field in certain iris recognitionsystems may be achieved, for example, by using multiple cameras thatbreak up an overall imaging volume into smaller imaging volumes. In suchcases, a field of view of interest may be steered into one or morecameras using mechanical devices such as mirrors or prisms. However,such mechanical devices may require additional power, may require moremaintenance, may reduce speed of an image capture process, and mayintroduce noise into captured images. Increasing depth of field,increasing field of view and increasing resolution of an imaging systemfacilitate iris recognition at large standoff distances. While currentlyavailable iris recognition imaging systems may not provide both largefield of view and high resolution, the inclusion of wavefront coding inthe imaging optics may improve performance in both of these aspects.

Iris recognition systems may use illumination sources in the nearinfrared for improved iris image contrast. Illumination levels of theseillumination sources should be maintained at a safe level over an entireimaging volume in order to prevent potential damage to eyes. Severalclasses of wavefront coding that may improve iris recognition systemsinclude a cosine form, a caustic cubic form, a higher order separableform and a higher order non-separable form. High modulation over aspatial frequency range of interest and a defocus range of interest aredesired for large standoff distance applications.

An exemplary task-based imaging system 1510 is the IHONS 1.1 system forobtaining data regarding a scene for use in the task of iris imagerecognition. In particular, in the IHONS 1.1 system, image datacapturing arrangement 1520 includes optics for imaging a wavefront ofelectromagnetic energy from the scene to an intermediate image,modifying phase of the wavefront (i.e., wavefront coding), detecting theintermediate image, and generating image data over a range of spatialfrequencies. For example, image data capturing arrangement 1520 mayinclude one or more imaging optics and a wavefront coding element;alternatively, the imaging optics and the wavefront coding element maybe integrated into a single optical element or the wavefront codingeffect may be distributed over one or more of the imaging optics. Also,detecting of the intermediate image and generating of the image data maybe performed by a single detector configured for convertingelectromagnetic energy incident thereon into electronic data.Furthermore, image data processing arrangement 1530 of the IHONS 1.1system cooperates with image capturing system 1520 to account for themodification of the wavefront effected by the wavefront coding elementand further performs the task of iris image recognition. Specifics ofthe IHONS 1.1 system is described in detail immediately hereinafter inassociation with FIGS. 16-39 and the task of iris recognition at a largestandoff distance.

A WFC design that is useful for iris recognition at a large standoffdistance is a class of higher-order non-separable polynomial functionsdesignated iris high-order non-separable (“IHONS”). This class offers acompromise between risk minimization and performance. The IHONS designhas similarities to the iris high-order separable (“IHOS”) design usedin a wavefront coding application for iris recognition at shorterstandoff distances, such as that described in R. Narayanswamy et al.,“Extending the imaging volume for biometric iris recognition,” Appl.Op., vol. 44, no. 5, pp. 701-712. The IHOS design specifically refers tothe use of a phase altering surface for wavefront coding, where thephase altering surface is mathematically expressible as:φ(x,y)=exp{−j[ƒ(x)+ƒ(y)]},  Eq. 1where ƒ(x) and ƒ(y) are high-order polynomials. While the IHOS design issuitable for iris recognition at small standoff distances, the IHONSdesign allows implementation of WFC modulation with a small number offilters over the operating standoff distance range.

A mathematical description of a class of pupil phase functions thatcharacterize the IHONS design is:

$\begin{matrix}{{{\phi\left( {x,y} \right)} = {\sum\limits_{i,{j = 0}}^{N}{x^{i}{\alpha\left( {i,j} \right)}y^{j}}}},} & {{Eq}.\mspace{14mu} 2}\end{matrix}$where: 1) φ is a phase function at each normalized spatial coordinate xand y (i.e., an entire spatial field is normalized by division by theradius (r) of the entrance pupil to the range between 0 and 1 in eachdimension x and y); 2) φ is Hermitian, that is, each coefficientα_(ij)=α_(ji); 3) at least some |α_(ij)|≧1 when i=0 or j=0, providing arelatively high modulation transfer function (MTF) in x and y; and 4)values for α_(ij) when i≠0 and j≠0 may be defined by Eq. 3:

$\begin{matrix}{{\sum\limits_{i,{j = 1}}^{N}{{{\alpha\left( {i,j} \right)}r^{{- i} - j}}}^{2}} < {{\sum\limits_{l = 0}^{N}{{{\alpha\left( {l,0} \right)}r^{- l}}}^{2}} + {{{{\alpha\left( {0,l} \right)}r^{- l}}}^{2}.}}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

An exemplary “IHONS 1.1” design used in examples of FIG. 17 through FIG.41 utilizes specific α_(ij) coefficients in the IHONS design defined inEq. 1. The α_(ij) terms are defined as follows. The first four termscorrespond to separable terms:

α(0,3)=α(3,0)=23.394

α(0,5)=α(5,0)=60.108

α(0,7)=α(7,0)=−126.421

α(0,9)=α(9,0)=82.128

The remaining four terms correspond to non-separable terms:

α(3,3)=5.021

α(5,5)=−21.418

α(7,7)=−310.749

α(9,9)=−1100.336

FIG. 16 shows a surface plot 1600 of an exemplary IHONS 1.1, calciumfluoride (CaF₂) WFC element, which is suitable for use in image datacapturing arrangement 1520 within imaging system 1510 of FIG. 15. Forexample, IHONS 1.1 WFC element may be incorporated into the imagingsystem shown in FIG. 14 as slidable elements 1430, additional elements1440 and 1450 and/or element 1460 for modulating the phase of thewavefront. Surface plot 1600 has dimensions in millimeters as theabscissa and the ordinate. The gray scale bar to the right side of thesurface plot has units of microns. Each contour represents a sagdifference of approximately 2 microns from a center region 1610 value ofzero. Regions 1620 have a sag value of approximately 12 microns. Regions1630 have a sag value of approximately −12 microns. The totalpeak-to-valley surface sag difference is 24.4 microns, for a total pathlength difference of 19.3 waves at λ=840 nm. The IHONS 1.1 WFC elementmay be manufactured, for example, using a fast-servo diamond cuttingmanufacturing process. Given the small clearance between lens elements,CaF₂ was selected as the substrate material. An alternative material,polymethyl methacrylate (PMMA), would be less costly but potentiallymore prone to deform, given a large form factor (e.g., 5 mm thicknessfor a 30 mm diameter element). At first glance, surface plot 1600 maynot appear very different from that of a separable, IHOS design;however, the IHONS 1.1 design shown here includes the cross-termcoefficients that provide considerable off-axis modulation, whichenhances the polar SNR, as will be described in further detailimmediately hereinafter.

It is known that the average human iris has a diameter of approximately12 mm. In order to facilitate iris recognition, the texture of the irisshould be sampled at a high spatial frequency. Therefore, irisrecognition algorithms generally have a recommended minimum number ofpixels across the iris diameter. FIG. 17 is a graphical plot 1700 of thenumber of pixels of an image sensor array that subtend an image of aniris as a function of the standoff distance. Plot 1700 has standoffdistance in meters as the abscissa and number of pixels across an irison the ordinate. FIG. 17 shows that, as standoff distance decreases, theimage of the iris gets larger such that the image subtends more pixelsof the image sensor array. While an interpolation process does not addinformation to the iris image, the interpolation does better conditionthe iris image data for recognition, thereby yielding betterdiscrimination in iris recognition.

FIG. 18 is a graphical plot 1800 showing a number of waves of defocus asa function of standoff distance range. Plot 1800 has standoff distancein meters as the abscissa and number of waves of defocus on theordinate. Vertical dashed lines at 2.1 and 2.4 meters standoff distanceindicate a standoff distance range selected for use in one example ofthe iris recognition imaging system of the present disclosure. Ratherthan selecting a best-focus position that minimizes a maximum number ofwaves of defocus within a distance range, the range has been selectedsuch that there is more defocus when the subject is closer. Thisselection equalizes an available SNR over the entire standoff distancerange, since imaging at higher spatial frequencies is required when theiris is farther away from the imaging system, while the MTF decreasesmonotonically with spatial frequency for the imaging system includingwavefront coding. As FIG. 18 shows, no more than five waves of defocusneed be corrected for the standoff distance range of interest.

Referring now to FIGS. 19-21, the PSFs and MTFs resulting from asimulated imaging system (e.g., imaging system 3300 of FIG. 33,discussed herein below) including the IHONS 1.1 wavefront coding elementare computationally analyzed to determine the expected systemperformance. PSFs are examined for compactness and invariance over animaging volume. MTFs are examined for modulation strength in spatialbands of interest across the desired standoff distance range discussedabove. The modulation (contrast) and SNR at the frequencies of interestare examined as functions of standoff distance and across all angularorientations, as depicted by the polar-MTF plot of FIG. 21.

FIG. 19 shows a set 1900 of simulated, through-focus, normalized PSFs atdifferent standoff distances (in meters and noted in the upper left-handcorner of each subimage) for the IHONS 1.1 imaging system. The PSFs arelogarithmically gray-scaled and thresholded for clear presentation. Asindicated in FIG. 18, the best-focus is at 2.27 m. Coma, as measured inone of the lenses used in the imaging system, was also included, butthis characteristic is not inherent in the IHONS 1.1 imaging system.Notably, the PSFs shown in FIG. 19 with IHONS 1.1 are similar to thoseexpected from a rectangularly-separable design with IHOS. That is,desirably, the PSFs resulting from the IHONS 1.1 imaging system do notchange significantly as a function of standoff distance, allowing theimplementation of iris recognition at the large standoff distance usingonly a small number of filters over the required range of standoffdistances.

FIG. 20 shows a set 2000 of simulated, through-focus MTFs at differentstandoff distances (in meters and noted in the upper left-hand corner ofeach subimage) for the IHONS 1.1 imaging system. The MTFs arelogarithmically gray-scaled and thresholded for clear presentation.Again, a sample of measured coma is included in the simulation forcompleteness, although the coma is not an inherent characteristic of theIHONS 1.1 imaging system. It may be noted in FIG. 20 that highmodulation exists in the vertical and horizontal directions but,contrary to a purely separable design (e.g., IHOS), diagonal andoff-diagonal modulations are slightly larger, especially as the objectmoves away from best-focus, where more modulation is desired. Thisfeature of the MTFs of the IHONS 1.1 imaging system, combined with theslow PSF variation as shown in FIG. 19, demonstrate the advantages ofthe weakly non-separable design, as provided by IHONS 1.1, over the IHOSsystem in this particular application to an iris recognition system at alarge standoff distance.

FIG. 21 shows a polar-MTF contour plot of the IRONS 1.1 system. Plot2100 has standoff distance in meters as the abscissa and polar angle inradians on the ordinate. The gray-scale contours of this plot representthe modulation of the spatial frequencies of interest (i.e., frequenciesassociated with a critically sampled object feature of 0.1 mm) as afunction of direction (vertical axis) and as a function of standoffdistance (horizontal axis), taking into account spatial frequencyvariation as a function of standoff distance.

For implementation of iris recognition at a large standoff distance, alldirections are, arguably, equally important. FIG. 22 is a plot 2200 ofmean contrast averaged over all directions that provides an accuratemeasure of performance. Plot 2200 has standoff distance in meters as theabscissa and contrast on the ordinate. FIG. 22 shows the mean contrastat spatial frequencies of interest as a function of standoff distance,averaged over all directions (−π to +π), for the IHONS 1.1 system of thepresent disclosure. As shown in FIG. 22, the contrast at the highestspatial frequencies of interest (corresponding to object detail of 0.1mm) is high. FIG. 23 shows a related plot 2300 of the mean SNR versusstandoff distance. The mean SNR, more so than the mean contrast, may becalculated and used as a quantitative measure of the system performance.

FIG. 24 shows a graphic representation 2400 of a filter used forprocessing captured WFC images using the IHONS 1.1 imaging system inaccordance with the present disclosure. The filter has been built usinga Wiener parametric method using an average of three PSFs captured closeto the best-focus position. Wiener filter parameters include a noiseparameter of 250 and an object detail of 1.2. A resulting noise gain is0.54, which indicates that the filter is smooth.

Image simulation is an important step in the design process of atask-based imaging system, such as iris recognition. FIG. 25 shows aflow diagram illustrating a process 2500 for generating simulatedimages. Process 2500 may be performed, for example, within image dataprocessing arrangement 1530 of FIG. 15; for instance, image dataprocessing arrangement 1530 may include software or firmware forperforming process 2500. Process 2500 for simulating images begins witha preparation step 2505 during which system initialization and othertasks are performed. A high resolution input image data 2510, includinga range of spatial frequencies, is Fourier transformed (e.g., by afast-Fourier Transform (FFT) method) in a step 2515 to yield a Fourierspace, input image spectrum 2520. High resolution defocused OTF data2525 and high resolution, pixel MTF data 2535 of the imaging system aredetermined, then multiplied with input image spectrum 2520 in a step2530 to generate a modified image spectrum of the high resolution image.Pixel sampling and low-pass filtering may be taken into account by themultiplication by the pixel MTF. OTF data may include measured wavefronterror of a sample lens.

Since defocus varies according to the standoff distance (d₀), the OTFmay be interpolated to have the same matrix size as the spectrum of thehigh resolution image. Knowledge of this matrix size may also beimportant for performing the real space conversion of the image data inan inverse Fourier transform step 2545. The OTF may be modified byaltering, for example, a wavefront coding element within the imagingsystem such that the SNR in the output image is further increased overother systems without the SNR. In step 2545, the modified image spectrumfrom step 2530 is converted into a modified image by inverse-FFT. Thismodified image may then be used to generate an output image. In a step2550, the image is resized by down-sampling to the final resolution,thereby taking the variable magnification (due to, for instance,variation in object distance) into account. Aliasing may also be takeninto account by down-sampling without low-pass filtering the image.Down-sampling may include, alternatively, processing the modified imagefor a given down-sampling origin and a commonly used sampling product,and then generating multiple aliased versions of the resized image byvarying the down-sampling origin within the down-sampling period. Theprocesses of down-sampling and origin variation are discussed at anappropriate point hereinafter in discussions related to FIGS. 28 and 29.An iris recognition algorithm may require an image that is a specificsize (e.g., 640×480 pixels). Since the original image may be at highmagnification, the area including the iris may be smaller than thissize. During a step 2555, the image may be zero padded, but this processmay result in unrealistic edges around the image. In order to yield morerealistic images, the simulated images may be padded with a copy oftheir external boundary lines instead. The boundary lines are thetopmost row, bottommost row, leftmost column and rightmost column of theimage. These boundary lines may be replicated until the image is filledto 640×480, therefore resulting in streaks around the borders. FIG. 30shows an example of these edge effects.

Finally in a step 2560, Poisson-distributed shot noise andGaussian-distributed read noise may be added to the image, using thesame noise parameters (e.g., full well count and read noise count)present in the actual detector. The result is an output image 2565 thatis a faithful reproduction of images actually captured by an IHONS 1.1system, with the exception of not representing detector saturation. Theoutput images may then be filtered with the selected filter kernel,producing images such as those shown in FIG. 30. The simulation processdoes not take into account detection saturation that may take place atspecular reflection spots inside the pupil and other areas in the image.The simulation algorithm of FIG. 25 includes effects of wavefront codingon defocused images, such that algorithmic recognition may be performedon the simulated images, consequently allowing prediction of overallsystem performance.

FIG. 26 presents a block diagram 2600 for an optimization method thatmay use a given parameter, such as polar-SNR, in order to optimize atask-based imaging system. FIG. 26 is identical to FIG. 2 of the abovereferenced U.S. patent application Ser. No. 11/000,819, and isreproduced here to illustrate a general approach to optical and digitalsystem design optimization. Design optimizing system 2612 may be used tooptimize a system design 2613, which includes both an optical systemdesign 2614 and a digital system design 2615. By way of example, opticalsystem design 2614 may be an initial optical prescription for awavefront coding element, such as that shown in FIG. 16, and digitalsystem design 2615 may be an initial design of a filter, such as thatshown in FIG. 24, used for signal processing images from the opticalsystem. Design optimizing system 2612 may function to generate anoptimized system design 2630. Optimized system design 2630 may includeoptimized optical system design 2632 and optimized digital system design2634. An exemplary optimized design is the herein described IHONS 1.1design.

System design 2613 is input to design optimizing system 2612 to create asystem model 2616. System model 2616 illustratively includes an opticalsystem model 2617 and a digital system model 2618 that represent,respectively, optical system design 2614 and digital system design 2615.Design optimizing system 2612 may simulate functionality of system model2616 to generate an output 2619. Output 2619 may for example include apupil map generated by simulation of optical system model 2617 and bitstream information associated with processing by digital system model2618.

Design optimizing system 2612 includes an analyzer 2620 that processesoutput 2619 to generate a score 2622. As above, analyzer 2620 mayutilize one or more metrics 2621 to determine score 2622. Metrics 2621pertain to both optical system model 2617 and digital system model 2618.Results from each metric 2621 may be weighted and processed by analyzer2620 to form score 2622. Weights for each metric 2621 may, for example,be specified by a user and/or algorithmically determined.

An optimizer 2623 processes score 2622 and determines the performance ofsystem model 2616 relative to goals 2626, which may, again, be specifiedby the user (e.g., user defined goals 2624, such as a target polar SNRvalue) for input to optimizer 2623. If system model 2616 is notoptimized, design optimizing system 2612 responds to output 2625 fromoptimizer 2623 to modify optical system model 2617 and/or output 2638from optimizer 2623 to modify digital system model 2618. If either ofsystem models 2617 or 2618 is modified, system model 2616 is againsimulated by design optimizing system 2612 and output 2619 is scored byanalyzer 2620 to generate a new score 2622. Optimizer 2623 thuscontinues to modify system models 2617 and 2618 iteratively until designgoals 2626 are achieved. For iris recognition, an example of a goal isto optimize the value of a polar-MTF within a set of spatial frequenciesof interest.

Once design goals 2626 are achieved, design optimizing system 2612 mayoutput an optimized system design 2630 that is based on system model2616 as modified by optimizer 2623. Optimized system design 2630includes an optimized optical system design 2632 and an optimizeddigital system design 2634, as shown. Optimized system design 2630 maytherefore include parameters that specify design objects of anelectro-optical system that meets goals 2626. Design optimizing system2612 may output a predicted performance 2640 that, for example,summarizes capabilities of optimized system design 2630.

A flowchart shown in FIG. 27 describes an exemplary optimization method2700 that uses the polar-SNR in order to optimize a task-based imagingsystem. Optimization method 2700 may be performed, for example, as apart of image data processing arrangement 1530 of FIG. 15; that is,image data processing arrangement 1530 may include software or firmwarefor performing optimization method 2700 in cooperation with image datacapture system 1520. Optimization method 2700 starts with a preparationstep 2705 during which system initialization and other tasks areperformed. An initial value of the optical merit function 2710 isdetermined by a user and becomes the initial value of a modified opticalmerit function 2715. During a step 2725, initial values of pupilfunction parameters 2720 along with the value of a modified opticalmerit function 2715 are input into an optical design software packagesuch as ZEMAX®, CODE V® or OSLO® (or other programs known in the art)for optimization. The pupil function parameters may then be modified bythe optical design software, providing modified pupil functionparameters 2730.

During steps 2735 and 2745, the OTF and the polar-SNR of the imagingsystem may be calculated taking into account a desired range of objectdistances (d₀) 2740 over the scene. Next, during a step 2755, thecalculated polar-SNR is compared to a goal polar-SNR 2750, which, formany applications, may be quite a simple function. For example, the goalpolar-SNR may be a straight line representing a minimum value of SNRsrequired within the range of operation of the imaging system. Next, ifthe calculated SNR is close enough to desired goal polar-SNR 2750(wherein the designer determines what is considered to be close enough),or if the calculated SNR is larger than the desired SNR, then theoptimization is complete and the process proceeds to a step 2760 and isfinished. Otherwise, the process proceeds via a loop pathway 2765 sothat the designer may create a new modified optical merit function 2725to account for deficiencies in the calculated polar-SNR (e.g., increasethe target modulation of the MTF of the imaging system at a givendirection). The optimization may be repeated until the design goal isreached.

FIG. 28 is a series of schematic diagrams 2800 showing the relativepositions of an original image, a PSF and a down-sampled image as seenby an imaging system. An original high resolution image 2810 is shown asa 2D array of small squares. If critically-sampled, image 2810 may beconsidered an ideal representation of the source scene. Down-sampledlow-resolution images (2820, 2820′ or 2820″) may represent the less thancritically-sampled digitized version of the source scene. Down-sampledlow-resolution images (2820, 2820′ or 2820″) are shown as a 2D array ofsquares that enclose nine smaller squares of the high resolution image.A PSF 2830 is shown as a black central dot with radial spokes andconcentric rings. PSF 2830 may be associated with a specific pixelwithin image 2810. In this example when down-sampled, the relativeorigins of the two images may be shifted to any of nine possiblepositions (3×3 to 1×1 down-sampling). This shifting may alter themapping of the PSF 2830 into the new image (2820, 2820′ or 2820″). Theshifting may also cause differing amounts of aliasing between the newimages and relative to the old image. All aliased positions may becalculated and used within analyzer 2620 of FIG. 26 as part of anoptimization method or within step 2550 of the simulation process ofFIG. 25.

FIG. 29 is set of plots 2900 detailing the effects of aliasing withregard to the varied origin of the down-sampling. Plot 2902 is a 2Dsimulation of a barcode-like pattern 2910. Pattern 2910 has a value ofone within the boundaries of the rectangles that form pattern 2910. Allother values are zero. A dashed line 2920 is a scan line that is sampledto create the data for plot 2904. Plot 2904 shows the curves associatedfor three variably shifted scan lines. A dotted line (curve 2930)represents a shift of zero pixels. A solid line (curve 2940) representsa shift of one pixel. A dashed line (curve 2950) represents a shift oftwo pixels. To generate each curve (2930, 2940 and 2950) the data ofpattern 2910 is convoluted with the appropriate shift with an examplePDF and then the convolved image is samples along scan line 2920. Bycomparing curves 2930, 2940 and 2950 it may be seen that the shapeswithin pattern 2910 are modified.

FIG. 30 shows a set of simulated final images 3000 that incorporate theeffects of a wavefront coding element and related processing. The finalimages were processed with an optimized set of filter parameters thatwere determined from the intermediate version of these same images, suchas derived using optimization 2700. Standoff distances in the subimagesin FIG. 30 vary from 2 to 2.5 meters, as indicated in the images of PSFsand MTFs shown in FIGS. 19 and 20 respectively. The standoff distancefor each subimage is noted in the upper left-hand corner of thatsubimage. Captured WFC images are then processed by iris recognitionsoftware, providing a metric of filter quality. Initially, multiplefilters were used over the range of standoff distances. However, it hasbeen determined that it is possible to meet all imaging specificationsusing the filter represented in FIG. 24. This reduction in the number offilters provides a significant advantage over the existing art.

Filtered images obtained by simulation are then identified by an irisrecognition algorithm, and an iris score (e.g., modified Hammingdistance (HD)) is generated for each iris image. FIG. 31 shows a plot3100 of resulting iris scores as a function of standoff distance for asimulated imaging system without wavefront coding. Plot 3100 hasstandoff distance in meters as the abscissa and Hamming Distance on theordinate. The solid horizontal line at an HD value near 0.31 shows theminimum required HD for positive recognition. Values of the standoffdistance from about 2.17 to 2.36 meters define a region over which asubject may be correctly recognized by the iris recognition system. Forevaluation of the IHONS 1.1 system, different templates were created. Atemplate is an averaged idealization of a subject's iris.

FIG. 31 shows the HD scores for two templates for identifying the samesubject. The data related to template A are shown as filleddiamond-shaped points in the plot. The data related to template B areshown as circular points. The data for both sets is averaged overmultiple measurements. Template B appears to provide slightly betterresults, since the iris recognition is then based on a slightly betterimage (i.e., larger visible iris region). The recognition range of thesimulated system without wavefront coding is about 18 cm.

FIG. 32 shows a plot 3200 of the resulting iris scores of the simulatedIHONS 1.1 system. Plot 3200 has standoff distance in meters as theabscissa and HD on the ordinate. The data related to template A areshown as filled diamond-shaped points in the plot. The data related totemplate B are shown as circular points. The data for both sets isaveraged over multiple measurements. FIG. 32 indicates that irisrecognition may be performed over an entire range of interest using asingle filter when IHONS 1.1 is used. Such simulated results are used atthe end of a design process to verify that the selected design,including but limited to the filter and WFC element, work as expected.

FIG. 33 shows an experimental setup 3300 used for verification of theIHONS 1.1 system. In the prototype task-based imaging system for irisrecognition verification, the image data capturing arrangement includesa lens system 3320, which in turn includes an IHONS wavefront codingelement (e.g., that shown in FIG. 16), a wide-angle lens with a 30 mmentrance pupil diameter and an effective focal length of 210 mm, and acamera 3330 (e.g., a CCD array). Lens system 3320 and camera 3330 aremounted onto an automated, rail system 3340. A subject 3310 rests his orher head on a tripod 2.05 meters away from rail system 3340. Camera 3330is a 10-bit CCD array with a resolution of 2048×2048. Lens system 3320further includes an illuminator including two illumination assemblies,each including four LEDs with a center wavelength of 840 nm, collimatedusing a Fresnel lens to yield a total irradiance of approximately 2mW/cm². Lens system 3320 images a wavefront of electromagnetic energyfrom subject 3310 to an intermediate image at CCD array 3330 while alsomodifying phase of the wavefront (i.e., wavefront coding). This phasemodification is designed such that the SNR of the resulting systemincluding wavefront coding is greater than the SNR of the imaging systemwithout wavefront coding. The eyes are individually aligned with respectto the field of view of the imaging system using optical posts mountedon top of a mini rail. Rail system 3340 includes a computer-controlledcoaxial screw rail used to vary the standoff distance. Rail system 3340is controlled by a controller 3350 that is responsive to a computer 3360running a MATLAB® script that captures ten images in short sequence at26 equally spaced positions from 2.05 to 2.45 meters.

Continuing to refer to FIG. 33, the image data processing arrangement isalso controlled by computer 3360. Another MATLAB® script performs thedecoding of the image using the kernel described in association withFIG. 24. A commercially available software package performs the task ofiris recognition using a variation of an algorithm by Daugman (see J. G.Daugman, “The importance of being random: statistical principles of irisrecognition,” Patt. Rec., 36, 279-291 (2003)). The images are saved to adatabase, and then analyzed by another MATLAB® script that processes theimages and assigns a score to each image based on pre-recorded highresolution templates. Experimental setup 3300 is converted from one withwavefront coding to one without wavefront coding by changing a lens (toone without wavefront coding effect) and refocusing. A similar setupcaptures PSFs, one difference being that the object is replaced by a 10μm pinhole. The pinhole is illuminated by a white light source, which isfiltered to block its visible spectrum while passing near-infraredlight.

FIG. 34 shows a series 3400 of experimentally measured PSFs using theIHONS 1.1 imaging system, in accordance with the present disclosure, fora range of standoff distances (indicated in meters in the upperleft-hand corner of each subimage). Intensity of a light source andexposure time of a camera were adjusted in order to keep PSFs close tosaturation, so as to use the maximum dynamic range of the system. Noisewas reduced by averaging 15 PSFs collected at each position. The camerauses a 10-bit sensor and non-linear noise removal was employed byreducing to zero all pixel values below the value of 18. PSFs werecollected at 26 equally spaced positions within the total range of therail (2.05 m to 2.45 m). The 26 PSF positions are summarized into thenine equally spaced PSFs shown in FIG. 34. The resemblance between theseexperimental PSFs (of FIG. 34) and the simulated PSFs (of FIG. 19)indicates good reproduction of the design, especially taking intoaccount that the noise-removing averaging often has the undesirableeffect of smoothing out the PSF.

System performance is further illustrated in FIG. 35 showing a series3500 of normalized, experimental MTFs, calculated by Fouriertransforming the experimental PSFs. It may be noted that theexperimental MTFs of FIG. 35 resemble the simulated MTFs of FIG. 20 andthat high on-axis modulation is maintained throughout a range ofstandoff distances, with only a slight drop at a far end of the range(2.45 m).

This drop in on-axis modulation is better visualized in a polar-MTF plot3600 of FIG. 36. Polar-MTF plot 3600 shows the modulation in alldirections as a function of distance only at the highestspatial-frequencies of interest, taking into account the variation inobject magnification with range. Again, there is a notable resemblancebetween the graphical plot shown in FIG. 36 and the simulated polar-MTFplot shown in FIG. 21. Although the fine details of plots 2100 and 3600vary, strong on-axis response (0, ±π/2, and ±π directions) as well asthe required magnitude of the off-axis directions are present in bothFIGS. 21 and 36.

Finally, FIG. 37 shows a graphical plot 3700 of the mean contrast overall directions at the highest spatial frequency of interest. This plotis of special interest to the iris recognition case given the equalimportance of resolving the iris object over all directions. This plotof FIG. 37 clearly shows the undesired drop in contrast at the farregion. Fortunately, this drop takes place at a range already beyond thetarget range, and it can be partially offset by moving the best focusfarther away (although to the detriment of the near range). The plot ofFIG. 37 also indicates that future designs may be improved byconfiguring the WFC element so as to move the two peaks further apart,thereby increasing the total range (although at the cost of reducing thelocal minimum at 2.17 m). A comparison of FIG. 37 with the simulatedplot of FIG. 22 also shows a remarkable resemblance, except for anarrowing of the distance between the contrast peaks (there is a smallchange in scale between the simulated and experimental plots).

The effect of the use of wavefront coding in iris recognition may besummarized as enabling the trade-off of HD for a wider range ofrecognition. This trade-off may be explained by the wider distributionof modulation (contrast) as a function of defocus provided by WFC. Inorder to accurately evaluate this trade-off, it is important to keepconstant all other parameters that affect the HD. These parametersinclude, but are not limited to: 1) illumination; 2) position of theeyelids; 3) presence of glasses, contact lenses or other objects in theoptical path; and 4) motion of the subject.

Such an evaluation may be performed for optimal imaging conditions, inwhich the subject is at rest, looking directly towards the camera withthe eyes wide open during the duration of image capture. The activenear-infrared illumination was used at high intensity, limited by eyesafety levels. Any variation in these parameters would either translateinto a drop in the SNR of the measurement or, more likely, into afailure of the iris recognition software to correctly segment the irisportion out of the resulting image. The sensitivity of the segmentationto experimental parameters is especially high in the low SNR cases(e.g., near the edges of the standoff distance range).

It should be noted that most iris recognition algorithms prefer tooperate with about 200 pixels across the iris image. Given the imagingparameters in actual imaging conditions, the number of pixels across theiris drops to less than 150 at the farthest ranges, as shown in FIG. 17.In order to compensate for this effect, all the images are linearlyinterpolated in experiment by an interpolation factor of 1.18. Allimages have been equally interpolated since, in practice, the irisrecognition system is not likely to be provided with the exact distanceto the subject's iris, meaning that the signal processing should berange independent. The interpolation factor was determined empirically,and it may be the subject of further optimization. Nevertheless, it wasnoted that the system consistently showed better performance withinterpolation than without interpolation.

FIG. 38 shows a plot of the Hamming distances as a function of distanceto the iris (measured from the iris to the first glass surface of theimaging system) for the imaging system without wavefront coding. Thepresence of a narrow valley with a sharp transition region is notable inFIG. 38, where the narrow valley corresponds to the region where defocusincurs a drop in modulation (contrast) at the spatial frequencies usedby the recognition algorithm. The flat region (2.2 to 2.3 m) close tobest-focus corresponds to the region where defocus results in a drop ofspatial frequencies that are higher than all the spatial frequenciesused by the algorithm. At each object position, ten images of each eyeare captured, processed and compared to the iris code corresponding tothat eye providing us with an averaged HD for each eye that is shown inplot 3800. Open circles connected by a solid line designate the righteye, and open squares connected by a dotted line designate the left eye.From the plot in FIG. 38, it may be deduced that a imaging systemwithout wavefront coding yields a recognition range of 14.9 cm at amaximum HD of 0.2 (dot-dash line at HD=0.2). The plot in FIG. 38 alsoallows verification of the accuracy of the simulated images bycomparison to the simulated Hamming distance plot shown in FIG. 31.

FIG. 39 shows a graphical plot 3900 of the HD as a function of the irisdistance for the imaging system including wavefront coding. FIG. 39includes a plot of Hamming distances as a function of standoff distancerange for an experimentally evaluated iris recognition system using theIHONS 1.1 imaging system, showing a doubling of the recognition range toapproximately 40 cm. Open circles connected by a solid line designatethe right eye, and open squares connected by a dotted line designate theleft eye. In this case, a shallow and broad valley is shown (from 2.05to 2.45 meters standoff distance), therefore effectively demonstratingthe trade-off of the lowest HD for an extended depth of field. Thistrade-off may be better understood if described in terms of SNR. If theexcess SNR is high enough, it is possible to drop it in order to extendthe depth of field without having any noticeable effect on the HD. Onthe other hand, if the SNR is just above the optimum value for correctiris recognition, as is often the case in systems that are designedwithout WFC, then any extension in the depth of field translates into adrop in the minimum HD. It may be noted that the imaging systemincluding WFC provides a recognition range of almost 40 cm at a maximumHD of 0.2 (dot-dash line at HD=0.2). Also, the variance of the Hammingdistances at a given position has increased considerably in the imagingsystem including wavefront coding over that of the imaging systemwithout wavefront coding. Finally, the plot in FIG. 39 allowsverification of the accuracy of the simulated images by comparison tothe plot shown in FIG. 32, thereby providing the confidence to usesimulated images to analyze the performance of future WFC designs.

As described above, WFC may be useful to effectively trade off HD (orSNR) for an extended range for the task at hand. This trade-off becomesespecially attractive when the system is provided with excess SNR, thusallowing an increase in, for instance, the iris recognition rangewithout a noticeable increase in the HD. Under the appropriatecircumstances, the recognition range in the imaging system including WFCmay be more than double that of a imaging system without wavefrontcoding, with the main limitation being the sporadic failure of the irisrecognition algorithm to correctly segment the iris image for the imagecaptured using WFC. These failures may be caused by, for example,algorithmic assumptions concerning the shape of the specular reflectionpresent in the pupil. These reflections assume a different shape whencaptured using an imaging system including WFC, which should be takeninto account for optimal performance. In addition, the weaklynon-separable form of the phase element yields slightly largermodulation off-axis (which is a characteristic of a non-separabledesign) while maintaining nearly non-varying PSFs over defocus (which isa characteristic of a separable design). This compromise yields asolution that is advantageous over those achieved using purely separabledesigns, and allowed the meeting all the design goals using a singlefilter over the entire design range.

Although each of the aforedescribed embodiments have been illustratedwith various components having particular respective orientations, itshould be understood that the system as described in the presentdisclosure may take on a variety of specific configurations with thevarious components being located in a variety of positions and mutualorientations and still remain within the spirit and scope of the presentdisclosure, The changes described above, and others, may be made in thetask-based imaging systems described herein without departing from thescope hereof. It should thus be noted that the matter contained in theabove description or shown in the accompanying drawings should beinterpreted as illustrative and not in a limiting sense. The followingclaims are intended to cover all generic and specific features describedherein, as well as all statements of the scope of the present method andsystem, which, as a matter of language, might be said to fall therebetween. Furthermore, suitable equivalents may be used in place of or inaddition to the various components, the function and use of suchsubstitute or additional components being held to be familiar to thoseskilled in the art and are therefore regarded as falling within thescope of the present disclosure. For example, although each of theaforedescribed embodiments have been discussed mainly for the case ofweakly separable phase functions, other WFC elements providing otherphase functions may be used in the task-based imaging system and stillprovide an improvement over currently available task-based imagingsystems without WFC.

Therefore, the present examples are to be considered as illustrative andnot restrictive, and the present disclosure is not to be limited to thedetails given herein but may be modified within the scope of theappended claims.

1. A method for generating an output image of a scene captured by adetector of a task-based imaging system, the detector including aplurality of pixels and the scene including at least one object locatedat a given object distance within a range of object distances, whichobject distance is defined as a distance between the object and thetask-based imaging system, the method comprising: capturing a highresolution image of the scene over a range of spatial frequencies;converting the high resolution image into an image spectrum of thescene; determining a defocused optical transfer function (OTF) of thetask-based imaging system over the range of object distances;determining a pixel modulation transfer function (MTF) over theplurality of pixels of the detector; multiplying the image spectrum withthe OTF and the MTF to generate a modified image spectrum of the scene;converting the modified image spectrum into a modified image of thescene; generating the output image from the modified image.
 2. Themethod of claim 1, wherein generating the output image includes forminga resized image from the modified image, and forming the output imagefrom the resized image.
 3. The method of claim 2, wherein forming theresized image includes down-sampling the modified image to a finalresolution, in accordance with the given object distance.
 4. The methodof claim 3, wherein down-sampling includes resizing the modified imagewithout low-pass filtering.
 5. The method of claim 3, whereindown-sampling comprises: processing the modified image for a givendown-sampling origin and a down-sampling period; and generating multiplealiased versions of the resized image by varying the down-samplingorigin within the down-sampling period.
 6. The method of claim 2,wherein the detector has shot noise and read noise characteristics, andwherein forming the output image comprises adding at least one of theshot noise and read noise characteristics to the resized image.
 7. Themethod of claim 2, wherein the resized image includes at least oneboundary line, the method further comprising padding the resized imageby replicating the boundary line to generate a padded image with adesired image size.
 8. The method of claim 1, further comprisingfiltering the output image with a filter kernel to generate a filteredimage.
 9. The method of claim 1, further comprising: from the outputimage, calculating a signal-to-noise ratio (SNR) over the scene;modifying the defocused OTF of the imaging system such that the SNR inthe output image is larger than that calculated from the output imagewithout modifying the defocused OTF.
 10. The method of claim 9, furthercomprising: averaging the SNR over a range of directions over the sceneto generate an average SNR; and altering the defocused OTF such that theaverage SNR in the output image is larger than that calculated from theoutput image without altering the defocused OTF.
 11. The method of claim10, wherein averaging the SNR comprises calculating a weighted averageSNR over the scene.
 12. The method of claim 11, wherein calculating theweighted average SNR includes varying a weighting factor of the SNR inaccordance with at least a selected one of a reduction in signalstrength and a reduction in incoherent imaging system modulation as afunction of the given object distance.
 13. The method of claim 11,further comprising setting a focus of the task-based imaging system at aposition corresponding to that at which an SNR calculated for smallestand largest object distance values in the range of object distances areequal.
 14. The method of claim 10, wherein altering comprises modifyingthe task-based imaging system to effect a pupil function of a form:${{\phi\left( {x,y} \right)} = {\sum\limits_{i,{j = 0}}^{N}{x^{i}{\alpha\left( {i,j} \right)}y^{j}}}},$where x and y are normalized, spatial coordinates, r is a radius of anentrance pupil and α(i,j) are pupil function coefficients for indices iand j with${{\sum\limits_{i,{j = 1}}^{N}{{{\alpha\left( {i,j} \right)}r^{{- i} - j}}}^{2}} < {{\sum\limits_{l = 0}^{N}{{{\alpha\left( {l,0} \right)}r^{- l}}}^{2}} + {{{\alpha\left( {0,l} \right)}r^{- l}}}^{2}}},\mspace{14mu}{and}$wherein at least one of coefficients α(i,j) has a value of at least onewhen at least one of indices i and j equals zero.
 15. The method ofclaim 1, further comprising post-processing the output image forperforming at least one task selected from the group consisting ofbiometric iris recognition, biometric face recognition, biometricrecognition for access control, biometric recognition for threatidentification, barcode reading, imaging for quality control in anassembly line, optical character recognition, biological imaging andautomotive imaging for object detection.
 16. A method for optimizing atask-based imaging system for obtaining data of a scene for use in atask over a range of object distances, the scene including at least oneobject located at a given object distance within the range of objectdistances, which object distance is defined as a distance between theobject and the task-based imaging system, the method comprising: 1)determining a target signal-to-noise ratio (SNR) of the task-basedimaging system; 2) specifying an initial set of pupil functionparameters and a merit function; 3) generating a new set of pupilfunction parameters based on the merit function; 4) calculating SNR overthe range of object distances; 5) comparing the SNR to a target SNR; and6) repeating steps 2) through 5) until the SNR is at least equal invalue to the target SNR.
 17. The method of claim 16, wherein determiningthe target SNR comprises determining a target polar-SNR, and whereincalculating comprises calculating a polar-SNR over the range of objectdistances.